Computer Graphics Fall 2005 COMS 4160 Lecture 16

Computer Graphics (Fall 2005) COMS 4160, Lecture 16: Illumination and Shading 1 http: //www. cs. columbia. edu/~cs 4160

To Do § Work on HW 3, do well § Start early on HW 4 § Discussion of midterm § But remember HW 3, HW 4 more important

Course Outline § 3 D Graphics Pipeline Modeling (Creating 3 D Geometry) Rendering (Creating, shading images from geometry, lighting, materials)

Course Outline § 3 D Graphics Pipeline Rendering Modeling (Creating 3 D Geometry) (Creating, shading images from geometry, lighting, materials) Unit 1: Transformations Weeks 1, 2. Ass 1 due Sep 22 Unit 2: Spline Curves Unit 4: Lighting, Shading Unit 3: Open. GL Weeks 5 -7. Ass 3 due Nov 10 Weeks 8, 9. Written Ass 1 due Nov 16 Weeks 3, 4. Ass 2 due Oct 7 Midterm on units 1 -3: Oct 26 Ass 4: Interactive 3 D Video Game (final project) due Dec 13

Rendering: 1960 s (visibility) § Roberts (1963), Appel (1967) - hidden-line algorithms § Warnock (1969), Watkins (1970) - hidden-surface § Sutherland (1974) - visibility = sorting Images from Fv. DFH, Pixar’s Shutterbug Slide ideas for history of Rendering courtesy Marc Levoy

Rendering: 1970 s (lighting) 1970 s - raster graphics § Gouraud (1971) - diffuse lighting, Phong (1974) - specular lighting § Blinn (1974) - curved surfaces, texture § Catmull (1974) - Z-buffer hidden-surface algorithm

Rendering (1980 s, 90 s: Global Illumination) early 1980 s - global illumination § Whitted (1980) - ray tracing § Goral, Torrance et al. (1984) radiosity § Kajiya (1986) - the rendering equation

Outline § Preliminaries § Basic diffuse and Phong shading § Gouraud, Phong interpolation, smooth shading § Formal reflection equation (next lecture) § Texture mapping (in one week) § Global illumination (next unit) For today’s lecture, slides and chapter 9 in textbook

Motivation § Objects not flat color, perceive shape with appearance § Materials interact with lighting § Compute correct shading pattern based on lighting § This is not the same as shadows (separate topic) § Some of today’s lecture review of last Open. GL lec. § Idea is to discuss illumination, shading independ. Open. GL § Today, initial hacks (1970 -1980) § Next lecture: formal notation and physics

Linear Relationship of Light § Light energy is simply sum of all contributions § Terms can be calculated separately and later added together: § multiple light sources § multiple interactions (diffuse, specular, more later) § multiple colors (R-G-B, or per wavelength)

General Considerations Surfaces are described as having a position, and a normal at every point. N 1 (x 1, y 1, z 1) N 2 (x 2, y 2, z 2) Other vectors used § L = vector to the light source light position minus surface point position § E = vector to the viewer (eye) viewer position minus surface point position

Diffuse Lambertian Term § Rough matte (technically Lambertian) surfaces § Not shiny: matte paint, unfinished wood, paper, … § Light reflects equally in all directions § Obey Lambert’s cosine law § Not exactly obeyed by real materials -L N

Meaning of negative dot products § If (N dot L) is negative, then the light is behind the surface, and cannot illuminate it. § If (N dot E) is negative, then the viewer is looking at the underside of the surface and cannot see it’s front-face. § In both cases, I is clamped to Zero.

Phong Illumination Model § Specular or glossy materials: highlights § Polished floors, glossy paint, whiteboards § For plastics highlight is color of light source (not object) § For metals, highlight depends on surface color § Really, (blurred) reflections of light source Roughness

Idea of Phong Illumination § Find a simple way to create highlights that are viewdependent and happen at about the right place § Not physically based § Use dot product (cosine) of eye and reflection of light direction about surface normal § Alternatively, dot product of half angle and normal § Raise cosine lobe to some power to control sharpness or roughness

Phong Formula -L R E

Alternative: Half-Angle (Blinn-Phong) N H § In practice, both diffuse and specular components for most materials

Outline § Preliminaries § Basic diffuse and Phong shading § Gouraud, Phong interpolation, smooth shading § Formal reflection equation (next lecture) § Texture mapping (in one week) § Global illumination (next unit) Not in text. If interested, look at Fv. DFH pp 736 -738

Triangle Meshes as Approximations § Most geometric models are large collections of triangles. § Triangles have 3 vertices, each with a position, color, normal, and other parameters (such as n for Phong reflection). § The triangles are an approximation to the actual surface of the object.

Coloring Between the Lines § We know how to calculate the light intensity given: § § surface position normal viewer position light source position (or direction) § How do we shade a triangle between it’s vertices, where we aren’t given the normal?

Flat vs. Gouraud Shading gl. Shade. Model(GL_FLAT) gl. Shade. Model(GL_SMOOTH) Flat - Determine that each face has a single normal, and color the entire face a single value, based on that normal. Gouraud – Determine the color at each vertex, using the normal at that vertex, and interpolate linearly for the pixels between the vertex locations.

Gouraud Shading – Details 1 § Inter-vertex interpolation can be done in object space (along the face), but it is simpler to do it in image space (along the screen). § 2 ways for a vertex to get its normal: § given when the vertex is defined. § take all the normals from faces that share the vertex, and average them.

Gouraud Shading – Details 2 Scan line Actual implementation efficient: difference equations while scan converting

Gouraud and Errors § I 1 = 0 because (N dot E) is negative. § I 2 = 0 because (N dot L) is negative. § Any interpolation of I 1 and I 2 will be 0. I 1 = 0 I 2 = 0 area of desired highlight

2 Phongs make a Highlight § Besides the Phong Reflectance model (cosn), there is a Phong Shading model. § Phong Shading: Instead of interpolating the intensities between vertices, interpolate the normals. § The entire lighting calculation is performed for each pixel, based on the interpolated normal. (Open. GL doesn’t do this, but you can with current programmable shaders) I 1 = 0 I 2 = 0

Problems with Interpolated Shading § Silhouettes are still polygonal § Interpolation in screen, not object space: perspective distortion § Not rotation or orientation-independent § How to compute vertex normals for sharply curving surfaces? § But at end of day, polygons is much easier than explicitly representing curved objects like spline patches for rendering